Find the standard deviation of the data set to the nearest tenth. (21,13,18,16,13,35,12,8,15)?

Question

a. 16.8
b. 7.8
c. 7.3
d. 5.7

(21,13,18,16,13,35,12,8,15)

Answer 1

The answer is b. Here's how to find it:

First find the mean:
(21 + 13 + 18 + 16 + 13 + 35 +12 + 8 +15) / 9 = 16.77777

Then find the deviations (I'll let you do these):
(21 -16.77777) =
(13 - 16.77777) =
(18 - 16.77777) =
(16 - 16.77777) =
(13 - 16.77777) =
(35 - 16.77777) =
(12 - 16.77777) =
(8 - 16.77777) =
(15 - 16.77777) =

Then, square all of those deviations, add them up, then divide by 9 if you want a population standard deviation, or divide by 8 if you want a sample standard deviation, then take the square root.

Answer 2

Mean= (21+13+18+16+13+35+12+8+15)/9
=151/9
=16.78

Therefore square of the deviations of all numbers from the mean:

(21-16.78)^2=4.22^2=17.8084
(13-16.78)^2=-3.78^2=14.2884
(18-16.78)^2=1.22^2=1.4884
(16-16.78)^2=-0.78^2=.6084
(13-16.78)^2=-3.78^2=14.2884
(35-16.78)^2=18.22^2=331.9684
(12-16.78)^2=-4.78^2=22.8484
(08-16.78)^2=-8.78^2=77.0884
(15-16.78)^2=-1.78^2=3.1684

Sum of all deviations=483.5556

Standard Deviation= sq.root(483.5556)

=21.99

Answer 3

sum of x is 151
sum of x^2 is 3017
n is 9 as there are 9 values
s= { [9(3017) - (151)^2] / [9 (9 - 1)]} ^ (1/2)
= (4352 / 72) ^ (1/2)
= 7.774602526
= 7.8 (b)

Answer 4

Type the numbers into Excel and use the stdev function

I get 7.8